求组合数

 1 typedef long long LL;
 2 const int N = 200005;
 3 
 4 bool prime[N];
 5 int p[N];
 6 int cnt;
 7 
 8 void isprime()
 9 {
10     cnt = 0;
11     memset(prime,true,sizeof(prime));
12     for(int i=2; i<N; i++)
13     {
14         if(prime[i])
15         {
16             p[cnt++] = i;
17             for(int j=i+i; j<N; j+=i)
18                 prime[j] = false;
19         }
20     }
21 }
22 
23 LL quick_mod(LL a,LL b,LL m)
24 {
25     LL ans = 1;
26     a %= m;
27     while(b)
28     {
29         if(b & 1)
30         {
31             ans = ans * a % m;
32             b--;
33         }
34         b >>= 1;
35         a = a * a % m;
36     }
37     return ans;
38 }
39 
40 LL Work(LL n,LL p)
41 {
42     LL ans = 0;
43     while(n)
44     {
45         ans += n / p;
46         n /= p;
47     }
48     return ans;
49 }
50 
51 LL Solve(LL n,LL m,LL P)
52 {
53     LL ans = 1;
54     for(int i=0; i<cnt && p[i]<=n; i++)
55     {
56         LL x = Work(n, p[i]);
57         LL y = Work(n - m, p[i]);
58         LL z = Work(m, p[i]);
59         x -= (y + z);
60         ans *= quick_mod(p[i],x,P);
61         ans %= P;
62     }
63     return ans;
64 }
65 
66 int main()
67 {
68     int T;
69     isprime();
70     cin>>T;
71     while(T--)
72     {
73         LL n,m,P;
74         cin>>n>>m>>P;
75         n += m - 2;
76         m--;
77         cout<<Solve(n,m,P)<<endl;
78     }
79     return 0;
80 }